Problem: Simplify the following expression: $k = \dfrac{5yz + 4xz}{2yz - z^2} - \dfrac{5z^2}{2yz - z^2}$ You can assume $x,y,z \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{5yz + 4xz - (5z^2)}{2yz - z^2}$ $k = \dfrac{5yz + 4xz - 5z^2}{2yz - z^2}$ The numerator and denominator have a common factor of $z$, so we can simplify $k = \dfrac{5y + 4x - 5z}{2y - z}$